Influence of mixing conditions on the rheological properties and structure of capillary suspensions

How bulk liquid viscosity shapes capillary suspensions

HYPOTHESIS

Capillary suspensions offer a new approach to generate novel materials. They are ternary liquid-liquid-solid systems characterized by particles connected by liquid bridges of one fluid suspended in a second immiscible bulk fluid. The viscosity of the bulk liquid can be modulated to customize the structure and rheological properties of capillary suspensions. Experiments and simulations: Using experiments and numerical simulations, we investigated capillary suspensions in the pendular state, using silica particles and water as a bridging liquid. To modulate the viscosity of the bulk fluid, we use different ratios of either dodecane and diisononyl phthalate, or silicone oils with varying chain lengths as bulk liquids. The rheological behavior was characterized using the maximum storage and loss moduli and the yielding behavior. This was related to structural changes of the systems, which was visualized using confocal laser scanning microscopy. In addition, we used Molecular Dynamics (MD) simulations to gain more insights into the behavior of two particles connected by a liquid bridge for various bulk liquids.

FINDINGS

Experiments show that higher bulk liquid viscosity reduces strength, yield stress, and yield strain in capillary suspensions, which is partly attributed to a reduced inter-connectivity of the percolating network. This is caused by the breakup of liquid bridges occurring at shorter distances in the presence of highly viscous bulk liquids, as indicated by numerical simulations.

Enhanced contact flexibility from nanoparticles in capillary suspensions

HYPOTHESIS

Sample-spanning particle networks are used to induce structure and a yield stress, necessary for 3D printing of porous ceramics and paints. In capillary suspensions, a small quantity of immiscible secondary fluid is incorporated into a suspension. By further adding nanoparticles with a range of hydrophobicities, the structure of the bridges and microparticle-microparticle contacts is expected to be modified, resulting in a tunable yield stress and shear moduli. Moreover, the compressibility of these samples, important in many processing and application steps, is expected to be sensitive to these changes.

EXPERIMENT

The nanoparticle hydrophobicity was altered and their position relative to the microparticles and the bridges was examined using confocal microscopy where the correlation between bridge size and network structure was observed. A step-wise uniaxial compression test on the confocal was conducted to monitor the microparticle movement and structural changes between capillary suspension networks with and without nanoparticles.

FINDINGS

Our observation suggests that nanoparticles induce the formation of thin liquid films on the surface of the microparticles, mitigating contact line pinning and promoting internal liquid exchange. Additionally, nanoparticles at microparticle contact regions further diminish Hertzian contact, enhancing the capacity for rearrangement. These effects enhance microparticle movement, narrowing the bridge size distribution.

Assembly and manipulation of responsive and flexible colloidal structures by magnetic and capillary interactions

The long-ranged interactions induced by magnetic fields and capillary forces in multiphasic fluid-particle systems facilitate the assembly of a rich variety of colloidal structures and materials. We review here the diverse structures assembled from isotropic and anisotropic particles by independently or jointly using magnetic and capillary interactions. The use of magnetic fields is one of the most efficient means of assembling and manipulating paramagnetic particles. By tuning the field strength and configuration or by changing the particle characteristics, the magnetic interactions, dynamics, and responsiveness of the assemblies can be precisely controlled. Concurrently, the capillary forces originating at the fluid-fluid interfaces can serve as means of reconfigurable binding in soft matter systems, such as Pickering emulsions, novel responsive capillary gels, and composites for 3D printing. We further discuss how magnetic forces can be used as an auxiliary parameter along with the capillary forces to assemble particles at fluid interfaces or in the bulk. Finally, we present examples how these interactions can be used jointly in magnetically responsive foams, gels, and pastes for 3D printing. The multiphasic particle gels for 3D printing open new opportunities for making of magnetically reconfigurable and "active" structures.

Quantifying the Workability of Calcium Sulfoaluminate Cement Paste Using Time-Dependent Rheology

Poor workability is a common feature of calcium sulfoaluminate (CSA) cement paste. Multiple chemical admixtures, such as set retarders and dispersants, are frequently employed to improve the workability and delay the setting of CSA cement paste. A quantitative assessment of the compatibility, efficiency, and the effects of the admixtures on cement paste workability is critical for the design of an appropriate paste formulation and admixture proportioning. Very limited studies are available on the quantitative rheology-based method for evaluating the workability of calcium sulfoaluminate cement pastes. This study presents a novel and robust time-dependent rheological method for quantifying the workability of CSA cement pastes modified with the incorporation of citric acid as a set retarder and a polycarboxylate ether (PCE)-based superplasticizer as a dispersant. The yield stress is measured as a function of time, and the resulting curve is applied to quantify three specific workability parameters: (i) the rate at which the paste loses flowability, (ii) the time limit for paste placement or pumping, marking the onset of acceleration to initial setting, and (iii) the rate at which the paste accelerates to final setting. The results of the tested CSA systems show that the rate of the loss of flowability and the rate of hardening decrease monotonously, while the time limit for casting decreases linearly with the increase in citric acid concentration. The dosage rate of PCE has a relatively small effect on the quantified workability parameters, partly due to the competitive adsorption of citrate ions. The method demonstrated here can characterize the interaction or co-influence of multiple admixtures on early-age properties of the cement paste, thus providing a quantitative rheological protocol for determining the workability and a novel approach to material selection and mixture design.

Effect of liquid volume fraction and shear rate on rheological properties and microstructure formation in ternary particle/oil/water dispersion systems under shear flow: two-dimensional direct numerical simulation

We numerically studied the rheological properties and microstructure formation under shear flow in a ternary particle/oil/water dispersion system. Our numerical simulation method was based on a phase-field model for capturing a free interface, the discrete element method for tracking particle motion, the immersed boundary method for calculating fluid-particle interactions, and a wetting model that assigns an order parameter to the solid surface according to the wettability. The effects of the water-phase volume fraction and shear rate on the microstructure and apparent viscosity were investigated. When the water-phase volume fraction was low, a pendular state was formed, and with an increase in the water-phase volume fraction, the state transitioned into a co-continuous state and a Pickering emulsion. This change in the microstructure state is qualitatively consistent with the results of previous experimental studies. In the pendular state, the viscosity increased with an increase in the water-phase volume fraction. This was due to the development of a network structure connected by liquid bridges, and the increase in the coordination number was quantitatively confirmed. In the case of the pendular state, significant shear thinning was observed, but in the case of the Pickering emulsion, no significant shear thinning was observed. It is concluded that this is due to the difference in the manner in which the microstructure changes with the shear rate. This is the first study to numerically demonstrate the microstructure formation of a ternary dispersion under shear flow and its correlation with the apparent viscosity.

Liquid-Suspended and Liquid-Bridged Liquid Metal Microdroplets

Liquid metals (LMs) and alloys are attracting increasing attention owing to their combined advantages of high conductivity and fluidity, and have shown promising results in various emerging applications. Patterning technologies using LMs are being actively researched; among them, direct ink writing is considered a potentially viable approach for efficient LM additive manufacturing. However, true LM additive manufacturing with arbitrary printing geometries remains challenging because of the intrinsically low rheological strength of LMs. Herein, colloidal suspensions of LM droplets amenable to additive manufacturing (or "3D printing") are realized using formulations containing minute amounts of liquid capillary bridges. The resulting LM suspensions exhibit exceptionally high rheological strength with yield stress values well above 10³  Pa, attributed to inter-droplet capillary attraction mediated by the liquid bridges adsorbed on the oxide skin of the LM droplets. Such liquid-bridged LM suspensions, as extrudable ink-type filaments, are based on uncurable continuous-phase liquid media, have a long pot-life and outstanding shear-thinning properties, and shape retention, demonstrating excellent rheological processability suitable for 3D printing. These findings will enable the emergence of a variety of new advanced applications that necessitate LM patterning into highly complicated multidimensional structures.

Structure-Property Relationship in Capillary Foams

The recently discovered capillary foams are aqueous foams stabilized by the synergistic action of colloidal particles and a small amount of oil. Characteristically, their gas bubbles are coated by a particle-stabilized layer of oil and embedded in a gel network of oil-bridged particles. This unique foam architecture offers opportunities for engineering new foam-related materials and processes, but the necessary understanding of its structure-property relations is still in its infancy. Here, we study the effects of particle wettability, particle volume fraction, and oil-to-particle ratio on the structure and selected properties of capillary foams and use our findings to relate measured foamability, foam stability, and rheological key parameters to the observed foam microstructure. We see that particle wettability not only determines the type of gel network formed but also influences the prevalence of oil droplets included within the foam. Our results further show that the stability and rheology of capillary foams are mainly a function of the particle volume fraction whereas the foamability and observed microstructure are sensitive also to the oil-to-particle ratio. These insights expand our fundamental understanding of capillary foams and will greatly facilitate future work on new foam formulations.

Nonequilibrium Structure Diagram of Pendular Suspensions under Large-Amplitude Oscillatory Shear

For pendular suspensions with particles in contact with immiscible secondary liquid bridges, the shear field significantly influences particle aggregates and networks. In this work, we study the structure of the pendular network and how the structure changes under large-amplitude-oscillatory shear. Using rheology and optical microscopy, we found unique network destruction followed by reconstruction with increasing strain. Two processes show different shear-field dependencies, strain-rate dependency for destruction and strain dependency for reconstruction. A nonequilibrium state diagram is constructed to show the phase behavior, where the critical particle concentration of sol-gel transition is dependent on the shear history and may depend on shear strain nonmonotonically. Two different mechanisms, shear-induced network breakdown at low strain and shear-induced agglomeration at high strain, are suggested to describe the nonmonotonic critical concentration under the upward strain sweep quantitatively.

Yield Stress Enhancement of a Ternary Colloidal Suspension via the Addition of Minute Amounts of Sodium Alginate to the Interparticle Capillary Bridges

Capillary suspensions are ternary solid-liquid-liquid systems produced via the addition of a small amount of secondary fluid to the bulk fluid that contained the dispersed solid particles. The secondary fluid could exert strong capillary forces between the particles and dramatically change the rheological properties of the suspension. So far, research has focused on capillary suspensions that consist of additive-free fluids, whereas capillary suspensions with additives, particularly those of large molecular weight that are highly relevant for industrial purposes, have been relatively less studied. In this study, we performed a systematic analysis of the properties of capillary suspensions that consist of paraffin oil (bulk phase), water (secondary phase), and α-Al₂O₃ microparticles (particle phase), in which the aqueous secondary phase contained an important eco-friendly polymeric binder, sodium alginate (SA). It was determined that the yield stress of the suspension increased significantly with the increase in the SA content in the aqueous secondary phase, which was attributed to the synergistic effect of the capillary force and hydrogen bonding force that may be related to the increase in the number of capillary bridges. The amounts of SA used to induce a significant change in the yield stress in this study were very small (<0.02% of the total sample volume). The addition of Ca²⁺ ions to the SA-containing secondary phase further increased the yield stress with possible gelation of the SA chains-in the presence of excess Ca²⁺ ions, however, the yield stress decreased because of the microscopic phase separation that occurred in the aqueous secondary phase. The microstructures of the sintered porous materials that were produced by using capillary suspensions as precursors were qualitatively well correlated to the rheological behavior of the precursor suspensions, suggesting a new method for the subtle control of the microstructures of porous materials using the addition of minute amounts of polymeric additives.

A New Solid-like State for Liquid/Liquid/Particle Mixtures with Bicontinuous Morphology of Concentrated Emulsion and Concentrated Suspension

Research in exploring the microstructures of the ternary liquid/liquid/particle mixture is still a challenging task due to the complex interface properties and compositions of each phase. In this work, we report a new kind of solid-like state for ternary mixtures after the addition of a surfactant, which has the bicontinuous morphology of two phases, that is, the concentrated emulsion and the concentrated noncolloidal suspension. The bicontinuous morphology was justified by optical microscopy and the unique two-step yielding behavior under large oscillatory shear flow, which has the yielding character of a noncolloidal suspension at smaller strain and that of a concentrated emulsion at larger strain. A phase diagram is constructed from the rheological measurements and morphological observations. The boundaries of the new solid-like state can be well predicted from three basic requirements on the glass forming or jamming conditions in the aqueous noncolloidal suspension phase, the aqueous emulsion phase, and the whole ternary mixture.

Lightweight Porous Glass Composite Materials Based on Capillary Suspensions

In this article, we present a simple, advanced method to produce lightweight tailor-made materials based on capillary suspensions that are made from locally bonded hollow glass spheres with a high total porosity in the range of 70% at apparent densities of 200 kg/m³, having a compressive strength of 0.6 MPa. The amount of added liquid and the particle surface treatment determine the network structure in the pastes and the resulting microstructure of the porous material in a straightforward manner. This structure has a strong impact on the porosity, pore size, and mechanical properties of the final body. The most promising porous materials were made of surface treated hollow glass spheres that create a sample-spanning network in the capillary state, where the added liquid wets the particles worse than the bulk fluid. These samples approach the density of natural balsa wood and they may find application in fields where either weight or structure are important, such as in insulation materials, filters, and membranes, as well as lightweight construction materials for automotive or aerospace engineering.

Structure of capillary suspensions and their versatile applications in the creation of smart materials

In this article, we review recent research in the field of capillary suspensions and highlight a variety of applications in the field of smart materials. Capillary suspensions are liquid-liquid-solid ternary systems where one liquid is only present in a few percent and induces a strong, capillary-induced particle network. These suspensions have a large potential for exploitation, particularly in the production of porous materials since the paste itself and the properties of the final material can be adapted. We also discuss the rheological properties of the suspension and network structure to highlight the various ways these systems can be tuned.

Radical polymerization of capillary bridges between micron-sized particles in liquid bulk phase as a low temperature route to produce porous solid materials

We present a generic and versatile low temperature route to produce macro-porous bodies with porosity and pore size distribution that are adjustable in a wide range. Capillary suspensions, where the minor fluid is a monomer, are used as pre-cursors. The monomer is preferentially located between the particles, creating capillary bridges, resulting in a strong, percolating network. Thermally induced polymerization of these bridges at temperatures below 100 °C for less than 5 hours and subsequent removal of the bulk fluid yields macroscopic, self-supporting solid bodies with high porosity. This process is demonstrated using methylmethacrylate and hydroxyethylmethacrlyate with glass particles as a model system. The produced PMMA had a molecular weight of about 500.000 g/mol and dispersity about three. Application specific porous bodies, including PMMA particles connected by PMMA bridges, micron-sized capsules containing phase change material with high inner surface, and porous graphite membranes with high electrical conductivity, are also shown.

Hardening of particle/oil/water suspensions due to capillary bridges: Experimental yield stress and theoretical interpretation

Suspensions of colloid particles possess the remarkable property to solidify upon the addition of minimal amount of a second liquid that preferentially wets the particles. The hardening is due to the formation of capillary bridges (pendular rings), which connect the particles. Here, we review works on the mechanical properties of such suspensions and related works on the capillary-bridge force, and present new rheological data for the weakly studied concentration range 30-55 vol% particles. The mechanical strength of the solidified capillary suspensions, characterized by the yield stress Y, is measured at the elastic limit for various volume fractions of the particles and the preferentially wetting liquid. A quantitative theoretical model is developed, which relates Y with the maximum of the capillary-bridge force, projected on the shear plane. A semi-empirical expression for the mean number of capillary bridges per particle is proposed. The model agrees very well with the experimental data and gives a quantitative description of the yield stress, which increases with the rise of interfacial tension and with the volume fractions of particles and capillary bridges, but decreases with the rise of particle radius and contact angle. The quantitative description of capillary force is based on the exact theory and numerical calculation of the capillary bridge profile at various bridge volumes and contact angles. An analytical formula for Y is also derived. The comparison of the theoretical and experimental strain at the elastic limit reveals that the fluidization of the capillary suspension takes place only in a deformation zone of thickness up to several hundred particle diameters, which is adjacent to the rheometer's mobile plate. The reported experimental results refer to water-continuous suspension with hydrophobic particles and oily capillary bridges. The comparison of data for bridges from soybean oil and hexadecane surprisingly indicate that the yield strength is greater for the suspension with soybean oil despite its lower interfacial tension against water. The result can be explained with the different contact angles of the two oils in agreement with the theoretical predictions. The results could contribute for a better understanding, quantitative prediction and control of the mechanical properties of three-phase capillary suspensions solid/liquid/liquid.

Fractal approaches to characterize the structure of capillary suspensions using rheology and confocal microscopy

The rheological properties of a particle suspension can be substantially altered by adding a small amount of a secondary fluid that is immiscible with the bulk phase. The drastic change in the strength of these capillary suspensions arises due to the capillary forces, induced by the added liquid, leading to a percolating particle network. Using rheological scaling models, fractal dimensions are deduced from the yield stress and from oscillatory strain amplitude sweep data as function of the solid volume fraction. Exponents obtained using aluminum-oxide-based capillary suspensions, with a preferentially wetting secondary fluid, indicate an increase in the particle gel's fractal dimension with increasing particle size. This may be explained by a corresponding relative reduction in the capillary force compared to other forces. Confocal images using a glass model system show the microstructure to consist of compact particle flocs interconnected by a sparse backbone. Thus, using the rheological models two different fractal dimensionalities are distinguished - a lower network backbone dimension (D = 1.86-2.05) and an intrafloc dimension (D = 2.57-2.74). The latter is higher due to the higher local solid volume fraction inside of the flocs compared to the sparse backbone. Both of these dimensions are compared with values obtained by analysis of spatial particle positions from 3D confocal microscopy images, where dimensions between 2.43 and 2.63 are computed, lying between the two dimension ranges obtained from rheology. The fractal dimensions determined via this method corroborate the increase in structural compactness with increasing particle size.

Suppressing Crack Formation in Particulate Systems by Utilizing Capillary Forces

Cracks, formed during the drying of particulate films, can reduce the effectiveness or even render products useless. We present a novel, generic approach to suppress crack formation in thin films made from hard particle suspensions, which are otherwise highly susceptible to cracking, using the capillary force between particles present when a trace amount of an immiscible liquid is added to a suspension. This secondary liquid preserves the particle cohesion, modifying the structure and increasing the drying rate. Crack-free films can be produced at thicknesses much greater than the critical cracking thickness for a suspension without capillary interactions, and even persists after sintering. This capillary suspension strategy is applicable to a broad range of materials, including suspensions of metals, semiconductive and ceramic oxides, or glassy polymeric particles, and can be easily implemented in many industrial processes since it is based on well-established unit operations. Promising fields of application include ceramic foils and printed electronic devices.